Question

Solve 2x^2 - x ≥ -5. Show your work.

Answer 1

Answer:

$(x-\frac{1}{4})^{2} \geq \frac{-39}{16}$

Step-by-step explanation:

Rewrite into standard form:

$2x^{2} -x+5 \geq 0$

Complete the square:

$2(x-\frac{1}{4} )^{2} + \frac{39}{8} \geq 0$

Subtract $\frac{39}{8}$ from both sides:

$2(x-\frac{1}{4})^{2} \geq \frac{-39}{8}$

Divide both sides by 2:

$(x-\frac{1}{4})^{2} \geq \frac{-39}{\frac{8}{2}}$

Simplify:

$(x-\frac{1}{4})^{2} \geq \frac{-39}{16}$